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Question

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?



A

a=0, b=7

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B

a=5, b=2

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C

a=1, b=6

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D

a=3, b=4

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Solution

The correct option is D

a=3, b=4


Mean of a, b, 8, 5, 10 is 6
a+b+8+5+105=6a+b=7....(i)
Variance of a, b, 8, 5, 10 is 6.80
(a6)2+(b6)2+(86)2+(56)2+(106)25=6.80

a212a+36+(1a)2+21=34          [Using eq.(i)]
2a214a+24=0a27a+12=0
a=3 or 4 b=4 or 3
The possible values of a and b are a=3 and b=4 or, a=4 and b=3


Mathematics

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